5. Exercise: Normal unknown and additive noise [I] Bookmark this page Exercises due Nov 9, 2022 06:59 EST Exercise: Normal unknown and additive noise 4 points possible (graded) As in the last video, let X : 9 + W, where 9 and W are independent normal random variables and W has mean zero. a) Assume that W has positive variance. Are X and W independent? Select an option a b) Find the MAP estimator of 9 based on X if 9 N N (1, 1) and W N N (O, 1), and evaluate the corresponding estimate if X = 2. : c) Find the MAP estimator of 8 based on Xif C') N N (0, 1) and W N N (0, 4), and evaluate the corresponding estimate if X = 2. = d) For this part of the problem, suppose instead that X : 28 + 3W, where G and W are standard normal random variables. Find the MAP estimator of (3 based on X under this model and evaluate the corresponding estimate if X : 2